Question

In Young's double slit experiment, the source is red light of wavelength $7\times {10}^{-7}m$. When a thin glass plate of refractive index $1.5$ at this wavelength is put in the path of one of the interfering beams, the central bright fringe shifts by ${10}^{-3}m$ to the position previously occupied by the $5^{th}$ bright fringe. The thickness $\left(in\mu m\right)$ of the plate is $x$. Find $x$.

Answer 1

In Young's double slit experiment, if an object is put in the path of the beam then the shift in fringes is given by

$shift=\frac{Dt(\mu -1)}{d}$

Also since the central bright fringe shifted to the position previously occupied by the 5th bright fringe, we have $shift=5\beta$

$⟹\frac{Dt(\mu -1)}{d}=5\beta$

$⟹t=\frac{5\beta d}{D}(\mu -1)$

We have fringe-width $beta=\frac{D\lambda }{d}$

$⟹t=\frac{5\lambda }{(\mu -1)}=\frac{5\times 7\times {10}^{-7}}{(1.5-1)}$

$⟹t=7\mu m$